The generator matrix

 1  1  1  1  1  1  1  1  1  1  X X^2  X X^2
 0 X^3+X^2  0 X^2  0 X^3 X^2 X^3 X^3 X^2 X^3+X^2 X^2  0  0
 0  0 X^3+X^2 X^2  0 X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3+X^2
 0  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0

generates a code of length 14 over Z2[X]/(X^4) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+100x^12+64x^13+200x^14+64x^15+67x^16+8x^18+8x^20

The gray image is a linear code over GF(2) with n=112, k=9 and d=48.
This code was found by Heurico 1.16 in 0.422 seconds.